Word Origin for chase

C17 (in the sense: frame for letterpress matter): probably from French châsse frame (in the sense: bore of a cannon, etc): from Old French chas enclosure, from Late Latin capsus pen for animals; both from Latin capsacase ²

Meaning "run after" developed mid-14c. Related: Chased; chasing. Older European words for "pursue" often also cover "persecute" (e.g. Greek dioko, Old English ehtan); modern ones often derive from words used primarily for the hunting of animals.

cut to the chase

Get to the point, get on with it, as in We don't have time to go into that, so let's cut to the chase. This usage alludes to editing (cutting) film so as to get to the exciting chase scene in a motion picture. [Slang; 1920s]